MODELING THE DEPLETION OF A RENEWABLE RESOURCE BY POPULATION AND INDUSTRIALIZATION: EFFECT OF TECHNOLOGY ON ITS CONSERVATION

Abstract In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of a renewable resource by population and industrialization with resource‐dependent migration. The effect of technology on resource conservation is also considered. In the modeling process, four variables are considered, namely, density of a renewable resource, population density, density of industrialization, and technological effort. Both the growth rate and carrying capacity of resource biomass, which follows logistic model, are assumed to be simultaneously depleted by densities of population and industrialization but it is conserved by technological effort. It is further assumed that densities of population and industrialization increase due to increase in the density of renewable resource. The growth rate of technological effort is assumed to be proportional to the difference of carrying capacity of resource biomass and its current density. The model is analyzed by using the stability theory of differential equations and computer simulation. The model analysis shows that the biomass density decreases due to increase in densities of population and industrialization. It decreases further as the resource‐dependent industrial migration increases. But the resource may never become extinct due to population and industrialization, if technological effort is applied appropriately for its conservation.     

Dynamics of a fishery system in a patchy environment with nonlinear harvesting

In this paper, a stock‐effort dynamical model with two fishing zones is discussed. The nonlinear harvesting function is assumed depending upon stock size as well as fishing effort. The migration of fish is considered between two zones. The harvesting vessels also move between zones to increase their revenue. The movements of fish and fishing vessels between zones are assumed to take place at a faster time scale as compared with processes involving growth and harvesting occurring at a slow time scale. The aggregated model is obtained for total fish stock and fishing effort. This aggregated (reduced) model is analyzed analytically as well as numerically. Biological and bionomic equilibria of the system are obtained, and criteria for local stability or instability of the system are derived. The impact of levels of taxation T on the fish population and on the revenue earned by the fishery is investigated. An optimal harvesting policy is also discussed using the Pontryagin's maximum principle. The aggregated model also exhibits Hopf and transcritical bifurcation with respect to the bifurcation parameter tax T. Numerical simulations are presented to illustrate the results.     

JOINTLY‐DETERMINED ECOLOGICAL THRESHOLDS AND ECONOMIC TRADE‐OFFS IN WILDLIFE DISEASE MANAGEMENT

ABSTRACT. We investigate wildlife disease management, in a bioeconomic framework, when the wildlife host is valuable and disease transmission is density‐dependent. Disease prevalence is reduced in density‐dependent models whenever the population is harvested below a host‐density threshold a threshold population density below which disease prevalence declines and above which a disease becomes epidemic. In conventional models, the threshold is an exogenous function of disease parameters. We consider this case and find a steady state with positive disease prevalence to be optimal. Next, we consider a case in which disease dynamics are affected by both population controls and changes in human‐environmental interactions. The host‐density threshold is endogenous in this case. That is, the manager does not simply manage the population relative to the threshold, but rather manages both the population and the threshold. The optimal threshold depends on the economic and ecological trade‐offs arising from the jointly‐determined system. Accounting for this endogene‐ity can lead to reduced disease prevalence rates and higher population levels. Additionally, we show that ecological parameters that may be unimportant in conventional models that do not account for the endogeneity of the host‐density threshold are potentially important when host density threshold is recognized as endogenous.     

CONTROL OF A METAPOPULATION HARVESTING MODEL FOR BLACK BEARS

ABSTRACT. We develop a metapopulation harvesting model that includes density‐dependent immigration and emigration and apply Pontryagin's maximum principle to derive an optimal harvesting and reserve design strategy. The model is designed to mimic the black bear population of eastern Tennessee and western North Carolina. Model results suggest that a forest region's population can be maintained despite high harvest levels due to emigration from a connected, un‐harvested park region. The amount of shared border between the park and forest region is important in determining the optimal harvesting strategy. This technique offers new insight on the spatial control of protected populations.     

斑须蝽种群空间分布格局Weibull分布的拟合

Weibull分布的概率密度函数为f(x) =(c/b) [(x -a) /b]c -1exp [(x a) /b]c ,x≥a。本文首次用于拟合班须蝽三代卵块的空间分布 ,8批抽样数据拟合结果表明班须蝽三代卵块在烟田的空间分布遵循Weibull分布。从而丰富了班须蝽种群空间格局的分布理论。同时 ,利用斑须蝽种群空间格局的资料探讨了Weibull分布的参数b、c与种群密度及种群聚集度之间的关系 ,结果表明 ,尺度参数b与种群密度、种群聚集度间均分别存在极显著的线性相关关系 ,形状参数c与种群密度存在极显著的正幂函数相关关系 ,与种群聚集度之间存在极显著负幂函数关系。     

VMCI下考虑顾客退货的供应链联合促销与协调

在允许顾客退货的环境下,以供应商管理寄售库存(VMCI)的供应链为对象,探讨了供应链的促销决策及协调问题。研究发现,集中情景下最优的寄售库存量与促销水平均高于分散情景下的对应值;根据在供应链运营过程中双方成员承担的不同风险设计的滞销补贴-双向促销成本分担契约可以实现供应链协调;期望退货费用不超过某一阈值时,全额退货策略优于不允许退货策略。此外,通过数值仿真揭示了顾客评估风险对利润及协调契约的影响。     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

Optimal Expenditure Patterns of a Double-Path Engineering Project

The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.     

Principal–agent problem for returns handling in a reverse supply chain with one manufacturer and two competing dealers

Focusing on the principal–agent problem in handling new-products returned by customers in a reverse supply chain with one manufacturer and two competing dealers, we investigate how a manufacturer motivates her dealers to exert their efforts to handle and sell the returned new-products using mathematical modelling. By taking into consideration the dealers’ individual rationalities, we design optimal incentive contracts under both symmetric and asymmetric information and obtain the following insights. In the symmetric information situation, dealers’ effort levels are identical to those maximising the expected overall profit of the supply chain. In the asymmetric information situation, however, the dealers’ effort levels are lower than the supply chain optimum. Further, in the case of intensifying competition between the dealers, their effort levels increase, while each dealer’ revenue share received from the manufacturer decreases and the risk, incentive and total agency costs of the entire supply chain tend to diminish. The revenue share is inversely correlated with return uncertainties. When we introduce another random environmental factor affecting returns into the incentive contract, this revenue share increases with a rise in dealers’ effort levels, while the above-mentioned costs of the entire system decline and this improves the supply chain system coordination. The incorporation of fairness into the principal–agent model promotes a further increase in the dealers’ effort levels, which is proved using the fixed-point theorem. Finally, we provide an example to demonstrate the main results.     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

考虑投资需求的易损耗物品质押融资决策模型

质押物发生损耗会降低质押物的市场价值,增加中小企业的违约风险,影响质押融资业务参与方的期望收益。同时,中小企业从金融机构获得的资金在扣除各项支出后如有剩余,还可以在资本市场进行短期投资以获利。基于此,本文设定质押物为易损耗物品且中小企业存在投资需求,构建存货质押融资决策模型。考虑两种情形:首先,给定金融机构的融资利率,决策中小企业的最佳投资回报率和物流企业的最优监管努力水平;其次,给定中小企业的投资回报率,决策金融机构的最佳融资利率和物流企业的最优监管努力水平。通过数值算例模拟决策变量的求解过程,敏感性分析验证了文中所给结论。     

企业聘用职业经理人的最优时机及其委托代理模型

认为尽管职业经理人的能力可能更强,但只有当企业规模大于临界规模时,企业才会选择聘用职业经理人.运用实物期权的方法,分析得到了企业聘用职业经理人的最优规模(时机),并基于此建立了最优分成制委托代理模型.分析结果表明,在企业考虑实物期权价值的情况下,增大了聘用职业经理人的临界规模,降低了最优分成比例,提高了代理人的努力水平.结果进一步显示,随着市场不确定性的增大,企业聘用职业经理人的临界规模增大,代理人的努力水平降低,最有分成比例增大.     

Optimization of a Multiperiod Resource Allocation Model

In this paper we examine multiperiod resource allocation problems, such as allocating a given marketing budget among T periods. The return functions of each period are assumed to be concave functions of the effective effort variable, which is composed of the expenditures in all previous periods and the present one. Assuming that the effect of an amount spent in period t is decreasing by a fixed rate in successive periods, necessary and sufficient conditions for a non-boundary optimal policy are derived. Under these conditions the optimal policy which maximizes total returns is obtained.     

MODELING THE POPULATION DYNAMICS OF A SUBTROPICAL UNGULATE IN A VARIABLE ENVIRONMENT: RAIN,COLD AND PREDATORS

ABSTRACT. A structured population model was developed for a large ungulate, the kudu (Tragelaphus strepsiceros). From a ten-year study in South Africa's Kruger National Park, relationships were established between annual survival rates of particular age classes and resource availability indexed by the ratio between annual rainfall and population biomass density. The projected population dynamics resembled that from a simple logistic model, but with the convexity of density dependence and intrinsic growth rate dependent upon assumptions about how age-specific mortality changed at low density levels. Moreover, rather than being a preset constant, the effective carrying capacity K wasa dynamic variable dependent upon rainfall. The model closely replicated the observed dynamicsof the kudu population over the study period, but failed to predict the observed kudu density at the start of the study from prior rainfall alone. Episodic cold weather extremeswere identified ashaving an additional influence on kudu dynamics. The model was also unsuccessful in predicting the changesin kudu abundance that occurred in Kruger Park subsequent to the study. Here changes in predation perhaps due to predator switching were a possible influence. These additional factorsinfluencing population dynamicswould not have been recognized without first establishing the effects of changing resource availability in response to rainfall fluctu-ationsbetween years. The elaborated model incorporating the effects of resource supply as influenced by rainfall, density dependence, background predation pressure and episodic severe weather hasbroader reliability than simpler modelsfor conservation applications, while still having a firm empirical foundation.     

Optimal impulsive harvesting policy for single population

In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence, the explicit expression and global attractiveness of impulsive periodic solutions for constant yield harvest and proportional harvest. Then, we choose the maximum sustainable yield as management objective, and investigate the optimal impulsive harvesting policies respectively. The optimal harvest effort that maximizes the sustainable yield per unit time, the corresponding optimal population levels are determined. At last, we point out that the continuous harvesting policy is superior to the impulsive harvesting policy, however, the latter is more beneficial in realistic operation.     

Modeling the effect of time delay on the conservation of forestry biomass

In this paper, we have studied the effect of time delay on conservation of forestry biomass by proposing a non-linear mathematical model. In the modeling process, it is assumed that the density of forestry biomass depletes due to the presence of human population and it is being conserved by applying some technological efforts. The analysis of model shows that the density of forestry biomass may be conserved if the technological effort is applied within the appropriate time. A longer delay in applying technological effort for its conservation destabilizes the system. The direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the mathematical results.     

ON THE OPTIMAL POLICY FOR COMBINING HARVESTING OF PREDATOR AND PREY

An optimal policy is sought for maximizing present value from the combined harvest of two ecologically dependent species, which would coexist as predator and prey in the absence of harvesting. Harvest rate for each species is assumed proportional to both stock level and effort. For a large class of biological productivity functions, it is established that the optimal equilibrium point in the phase-plane of stock levels must be a saddle-point. For quadratic productivity functions, a combination of analytical reasoning and numerical experiment is used to show that first and second order necessary conditions for optimality are satisfied by a unique approach to equilibrium, which must therefore be optimal. The corresponding control law is given, and an apparent suggestion of two previous authors concerning the policy is shown to be inappropriate. The optimal policy enables an estimate to be made of the true loss of resource value due to a catastrophic fall in stock level.     

面向网络外部性特征产品的供应链动态竞争策略研究

当产品具有网络外部性的特征时,该产品的规模收益特征对利润、产品价格和需求等因素都会产生重大影响。首先,通过将网络规模建立为网络成本投入的微分方程,分别构建了分散与集中式决策下的动态供应链模型。其次,以供应链的利润最大化为前提,利用微分博弈导出生产量、批发价、零售价和投入努力值的最优策略。结论表明:在生命周期的前部分,集中决策情形的供应链系统利润和产品价格低于分散决策情形,但越往后,其价格和利润都将逐步超过分散决策情形,且差距越来越大。     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.